It turns out that a similar interpolation scheme based on weighted \(k\) -NN can be shown to be consistent for both regression and classification and indeed to be optimal in a certain statistical sense (see [1]} for convergence rates for regression and classification and the follow-up work [2]} for optimal rates for regression). The scheme can be viewed as a type of Nadaraya-Watson [3]}, [4]} predictor. It can be described as follows. Let
\(K({\mathbf {x}},{\mathbf {z}})\)  be a singular kernel, such as
\(K({\mathbf {x}},{\mathbf {z}})=\frac{1}{\Vert {\mathbf {x}}-{\mathbf {z}}\Vert ^{\alpha }},~\alpha >0, \) 
